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(D) We know that angular momentum $L = m v R$ ... $(i)$For a planet revolving around the sun,the gravitational force provides the necessary centripeta

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$0.5$

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(D) We know that angular momentum $L = m v R$ ... $(i)$For a planet revolving around the sun,the gravitational force provides the necessary centripetal force:$\frac{m v^2}{R} = \frac{G M m}{R^2}$$v^2 = \frac{G M}{R}$$v = \sqrt{\frac{G M}{R}}$ ... (ii)Substituting equation (ii) into $(i)$:$L = m 	imes \sqrt{\frac{G M}{R}} 	imes R$$L = m \sqrt{G M R}$Since $m$,$G$,and $M$ are constants,we have:$L \propto \sqrt{R}$$L \propto R^{1/2}$Comparing this with $L \propto R^n$,we get $n = 0.5$.

Assuming that the earth is revolving around the sun in a circular orbit of radius $R$,the angular momentum is directly proportional to $R^{n}$. The value of $n$ is

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